From previous lectureLinear Span & SubspaceA linear spanof a set of vectors {v, v, …, v} in Rn12k• it is a subset of Rndenoted byspan{v1, v2, …, vk}• it contains all linear combinations of v1, v2, …, vk•it±“extends” the vectors to a linear object (that contains the origin)A subset of Rnis a subspace:±is±a±linear span of some vectors in Rn• it must contain the zero vector±±closed under additionChapter 3Vector Spaces3±±closed under scalar multiplication

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ection 3 3Section 3.3Linear IndependenceObjectivehat is a nearly independent/dependentet?• What is a linearly independent/dependentset?• How to show that a set is linearly (in)dependent?• What are some conditions on linearly (in)dependent sets?Other terminologiesChapter 3Vector Spaces5“redundant” vectors

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